When oil drills are successful, they release oil (possibly with natural gas) that has been trapped under a layer of rock. But what replaces the oil that has been released? Certainly there can’t be a vacuum, or the oil would be sucked back down. And there can’t be vents, or the oil would have come upward on its own. Does underground water seep into those areas, settling beneath the oil and pushing it upward?
Either the ground subsides, or water leaks in. In some cases, water is actually injected into the well in conjunction with oil drilling.
Ground subsidence occurs even in situations where there is much less overlying pressure. For example down in the Houston area, there’s a lot of groundwater pumped from relatively shallow wells, resulting in ground subsidence.
Also, as the reservoir decreases, seawater may be purposefully injected to push out what’s left (“improve oil displacement”).
The situation is not the same all over. When liquid resources are removed they may come out naturally under pressure as is the case with the current leaking well or they may need to be pumped. There are situations where the formations collapse a bit in unsupported places. (It happens more with coal mining areas.) Then there are formations where the oil and gas exists in a porousity that can support itself with the missing hydrocarbons. Generally, the oil is far enough down that no top settling is noticed. However, research shows that in large areas of oil production, the elevation of vast areas does shrink down to accommodate missing resources. While water and steam are injected in some wells to increase production, water does not usually naturally flow into the voids because the water table is far above the hydrocarbon layer. When the wells are drilled, they are lined with tubing that separates the vertical layers so water will not go down to the open areas and vise versa. When the well is diminished, it has to be plugged. The hole is filled with cement to prevent contamination. The greater fear is that hydrocarbons will infiltrate into the water table and destroy it. Plugging prevents this.
Here’s a (mercifully brief) fairly interesting paper on oil fields and subisdence eathquakes.